I figured out an easy way to post timestamps next to the text strings in my icon game, but I'm not sure if there's any way to fetch the time from the user's system to post it there. Is there any way to do this currently in Dream Maker, or would I have to pester Dantom to add it for an upcoming version?

I think he meant that he wanted to get the time from the player's computer so he could do something with their time offset. If that is the case, then no there is no current way, but you could have the player input their time offset when they join.